Advertisements
Advertisements
Question
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
Solution
|A| = `|("a", "b"),("c", "d")|`
= ad – bc
∴ |A|−1 = `1/("ad" - "bc")` .......`[∵ |"A"^-1| = 1/|"A"|]`
APPEARS IN
RELATED QUESTIONS
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(2,-4),(3,1)]`, then the adjoint of matrix A is
Choose the correct answer from the given alternatives in the following question:
For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals
Choose the correct answer from the given alternatives in the following question:
If A−1 = `- 1/2[(1,-4),(-1,2)]`, then A = ______.
Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.
Find the inverse of the following matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.
Fill in the blank :
If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`
State whether the following is True or False :
Singleton matrix is only row matrix.
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
If A = `[(3, 1),(5, 2)]`, and AB = BA = I, then find the matrix B
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`
If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
If A = `[(0, 1),(2, 3),(1, -1)]` and B = `[(1, 2, 1),(2, 1, 0)]`, then find (AB)−1
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
If A = [aij]2×2, where aij = i – j, then A = ______
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-1.
The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
If A is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A-1 = ______.
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If AB = I and B = AT, then _______.
If A = `[(2, -3, 3),(2, 2, 3),(3, "p", 2)]` and A–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.
If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is ______.
The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.
If A = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.